2 PROCEDURE

The vehicle geometry selected was a Range Rover 2000 model. In the process of FE modeling the following assumptions were made:

1.The structure of the passenger compartment is modeled taking into consideration some of the curved surfaces. However, due to complexities of creating the model, some of the geometry is created by using straight lines.

2.As a qualitative picture of the modal response was aimed, the structure is assumed to be simply supported rather than modeling the accurate vehicle suspension. Moreover, the material properties are assumed to correspond to a lightweight metal without reference to the actual materials present in the cabin.

3.The laminated glass for the windshield consists of two glass layers and is placed between a plastic foil made of polyvinyl butyral. Also, the windshield is indirectly bonded to the vehicle body with the use of rubber seals. In the model, the windshield is assumed to be made of a single layer of glass and is directly connected to the vehicle body.

4.The materials for both metal structure and the windshield are assumed to be linearly elastic, as the modal analysis performed ignores any nonlinearity.

5.The effect of seats and other internal parts in the cabin is not taken into account.

The material properties for the structure are assumed to be Young’s modulus E=70 GPa, Poisson’s ratio ν=0.29;and density ρ=2700 kg/m3;the windshield properties are assumed to be Young’s modulus E=64 GPa, Poisson’s ratio ν=0.17;and density ρ=2400 kg/m3;the air properties are density ρf=1.21kg/m3, and speed of sound c=340 m/s.

For the system analyzed, FLUID30 (3D element) was used for creating the finite element model of the acoustic cavities. This element has 8 corner nodes with 4 degrees of freedom(DOFs) per node: 3 translational displacements in the nodal x, y, and z directions, and pressure. The translational DOFs are applicable only at nodes which are on the fluid-structure interface. For modeling the thin-walled structures, SHELL63 elements were used. These are 4-node, 3D elastic shells with both bending and membrane capabilities. In this application, the bending version of the elements was used. The SHELL63 element has 6 DOFs at each node: 3 translations in the nodal x,y and z directions and 3 rotations about the nodal x, y and z axes. The choice of this specific shell element was determined by its compatibility with the acoustic element.

The acoustic cavity was discretized utilizing the two versions of the acoustic element: (1) FLUID30 interfacing structure with four DOFs per node, and (2) FLUID30 possessing only one DOF per node, namely the unknown acoustic pressure. The layers of elements external with respect to the cavity were of type (1); the rest of the fluid domain was modeled by the normal type (2). In order to switch on the creation of coupling matrices on the wetted surfaces, a fluid-structure interface (FSI)flag was issued for all shell and fluid elements in contact. After mesh quality studies the final FE model comprised 4505 acoustic elements and 2009 shell elements of approximate size 0.1 m. The passenger compartment model is shown in Fig. 1.

Figure 1 FE model of vehicle compartment

3 ANALYSIS

3.1 Acoustic-Structure Coupling

The FE code ANSYS introduces several assumptions for a finite element representation of an acoustic space: (1) the fluid is considered to be compressible and inviscid, but without mean flow velocity; and (2) the mean fluid density and pressure are assumed to be uniform throughout the acoustic field.

Having created a particular structure-acoustic model, the final assembled set of equations takes the following shape:

Where

[M]= the assembled structural mass matrix,

[K]=the assembled structural stiffness matrix,